Function Operations and Transformations

This video tutorial covers a quiz review on size changes and composition of functions. It begins with solving a composition of functions problem, followed by evaluating functions using a calculator. The tutorial then explores transformations, scale changes, and finding the domain of composite functions. It also discusses inverse functions, transformations, and writing scale changes. The video concludes with proving whether two functions are inverses.

What is the main focus of the first question in the video?

• Graphing a function

• Composition of functions

• Finding the domain of a function

• Simplifying a single function

When simplifying f(g(x)), what is the first step according to the order of operations?

• Addition

• Subtraction

• Exponentiation

• Multiplication

What is the result of g(17) when g(x) = 4x - 3?

• 63

• 65

• 68

• 70

In a translation transformation, what happens to the y-coordinate?

• It is divided by 3

• It remains unchanged

• It is multiplied by 3

• It is increased by 4

What must be true for the expression under a square root to ensure the domain is valid?

• It must be negative

• It must be an integer

• It must be positive or zero

• It must be a fraction

What is the inverse of the point (-4, -9) on a graph?

• (-9, 4)

• (9, -4)

• (-4, 9)

• (-9, -4)

How do you write a scale change that shrinks horizontally by a factor of 1/2?

• Divide y by 2

• Multiply y by 2

• Divide x by 2

• Multiply x by 2

What is the effect of applying a scale change of x/6 to a function?

• It stretches the graph vertically

• It compresses the graph horizontally

• It compresses the graph vertically

• It stretches the graph horizontally

What is the domain of the inverse function y = (x - 9)^2 + 4?

• All real numbers

• x ≥ 9

• x ≥ 4

• x ≤ 4

What must be true for two functions to be inverses of each other?

• f(g(x)) = 0

• f(g(x)) = g(f(x))

• f(x) = g(x)

• f(g(x)) = x and g(f(x)) = x